Abstract
This article analyzes the key challenges encountered by teachers and students in the process of teaching and learning the fundamentals of mathematical analysis in school settings. The study was conducted among mathematics teachers and high school students studying introductory analysis. The authors identified the topics that cause the most significant difficulties for students, including solving differential equations, integration, as well as abstract concepts such as limits and derivatives. It is shown that students experience difficulties in understanding the theoretical foundations and applying concepts in practice, especially when there are insufficient visualization and lack of connection to real-world problems. Teachers’ perspectives additionally revealed methodological barriers, including time constraints, limited access to modern didactic resources, poor preliminary preparation of students, and the gap between university-level training and school-level realities. The influence of factors such as teaching experience, education level, and qualification category of mathematics teachers on their perception and interpretation of pedagogical challenges has been analyzed. Conclusions are drawn about the need to update university course content, strengthen the practice-oriented approach, and provide systematic support for novice teachers. The findings of the study can be used in the development of methodological recommendations and in the design of professional development programs for in-service teacher training.